The Best Supporting Actor award should actually be titled
"the best performance by an actor in a supporting role."

In 1936, the acting awards were expanded to start recognizing
supporting roles. Best Supporting Actor Oscars are traditionally given
to actors who stand out in small roles.

It is quite common that the Best Supporting Actor
winner is either an older, established performer, or a young, inexperienced
actor. Throughout Academy history, most of the winners in
this category usually have no previous Oscar wins.

The Top Best Supporting Actor Winner:

Within five years, Walter Brennan won three Best
Supporting Actor awards. He was the first and - to date - is
the only performer to win three supporting awards (and within the shortest
period of time - five years! And his three wins were in the category's
first five years). Therefore, he was also the first to win three acting Oscars and the first Best Supporting Actor Oscar recipient.

The Top Best Supporting Actor
Oscar Winner

Best Supporting Actor Wins

Walter Brennan
4 career nominations
(4 B.S.A. noms),
3 wins

Come and Get It (1936)
Kentucky (1938)
The Westerner (1940)

Six other actors have received two Best
Supporting Actor awards (among them is one performer who has won
a consecutive statuette,
Jason Robards).

Four actors have received four Best Supporting Actor nominations, although only two of them won subsequent awards. The two actors with the most Best Supporting Actor nominations (with no wins) include Arthur Kennedy and Claude Rains.

Actors with the most Best Supporting
Actor nominations (in parentheses) include:

Walter Brennan (4) - with three wins (Come and Get It (1936), Kentucky (1938),
The Westerner (1940)); also nominated in 1941

Victor McLaglen was the first performer to be
nominated for a Best Supporting Oscar (for
The Quiet Man (1952)) after having already won the Lead Performance
Oscar for The Informer (1935).

Posthumous Winner:

The only actor to win a posthumous acting Oscar in a supporting role was Australian actor Heath Ledger for his role as The Joker in The Dark Knight (2008). He was the second actor to win a posthumous acting Oscar - the first was Peter Finch, who won Best Actor for his role as Howard Beale in Network (1976).

Multiple Nominations:

No single performer has ever won two performing awards in the
same year. There have been a total of eleven performers
who are double nominees - that means that they have received two acting nominations in the same year. Three were actors and eight were actresses (wins are
marked with *). (See the Best Supporting
Actress section for eight actresses who have duplicated the
feat.) Of the 11 performers (actors and actresses) who've been recognized with nods for two performances in the same year, seven of them ended up winning one of the trophies.

Double nominees usually win in one category (i.e., double nominees Al Pacino and Jamie Foxx won as
Best Actor, and Fitzgerald won as Best Supporting Actor - see below).

In only one case, an actor (Barry Fitzgerald) was simultaneously nominated in two performance categories for the same film. [The Academy would prevent this in future years by not allowing a double
nomination for the same performance.] He was the only actor simultaneously nominated in both the Best Actor and Best Supporting Actor categories for the same film and performance:

Barry Fitzgerald was nominated for both Best Actor and Best Supporting
Actor* for Going My Way (1944)

In a few instances, actors have been nominated for Best
Actor and Best Supporting Actor for different films in the same year. The two male actors who accomplished this feat were Al Pacino, and Jamie Foxx. Al Pacino was the first actor to be nominated for Best Actor and Best Supporting Actor in two different roles. And Jamie Foxx was the only African-American performer to have two Oscar nominations in one year:

Al Pacino (Best Actor for Scent of a Woman (1992)*
and Best Supporting Actor for Glengarry Glen Ross (1992))

George C.
Scott in his third screen appearance in The Hustler (1961) received his second supporting nomination in 1962 - after his first nomination received in 1960 for Anatomy of a Murder (1959). (His first film was The Hanging Tree (1959).) He became the first actor to decline his Oscar nomination - in protest of fellow actors' practice of campaigning for awards, calling the awards demeaning and self-serving. When Scott received another Oscar nomination (and won) as Best Actor for Patton (1970), he declined to accept the nomination and the award, because he did not feel himself to be in any competition with other actors, calling it a "meat parade."

Film Debut Nominees/Winners of Best Supporting Actor Oscars:

Only three actors have won the Best Supporting Actor
Oscar for their debut performance (in a feature film), while others received a nomination
for a substantial role in a film debut (a sampling):

On
The Waterfront (1954) - Lee J. Cobb, Karl Malden, and
Rod Steiger (all lost to Edmond O'Brien in The Barefoot
Contessa (1954)) - it was the first film to earn three
Oscar nominations for Best Supporting Actor

Only ten black performers have
won the Oscar in the supporting category (four Best Supporting Actor,
six Best Supporting Actress). Only four black actors have won the
Best Supporting Actor Oscar:

Louis Gossett, Jr. for An Officer and a Gentleman
(1982)

Denzel Washington for Glory (1989)

Cuba Gooding, Jr. for Jerry Maguire (1996)

Morgan Freeman for Million
Dollar Baby (2004)

Only fifteen awards have been won by African-Americans
(or blacks) in both lead and supporting categories (four Best Actor,
one Best Actress, four Best Supporting Actor, and six Best Supporting
Actress).

Jamie Foxx also set a record for being
the first black to debut as a nominee in two categories in the
same year, lead and supporting, for Ray (2004) and Collateral
(2004). Morgan Freeman's Best Supporting Actor
win for Million
Dollar Baby (2004), paired with Foxx's Best Actor win for Ray
(2004), was the first time that African-American actors
won in their respective categories in the same year.

Latino, Asian and Other Ethnic-Minority
(Non-English) Performers:

There have only been a few Best Supporting
Actor Oscar wins by ethnic/other minority (non-English) performers, or by actors in foreign-language performances:

Austrian-born Christoph Waltz won his second Best
Supporting Actor Oscar for Django Unchained (2012)

Austrian-born Christoph Waltz won Best Supporting Actor for Inglourious Basterds (2009) - his performance was in German and French as well as English

Spanish-born actor Javier Bardem won Best
Supporting Actor for No Country for Old Men (2007)

White performer Jeff Chandler was nominated as Best
Supporting Actor for playing the role of Apache chief Cochise in Broken
Arrow (1950)

South African-born Cecil Kellaway was nominated twice
for Best Supporting Actor: for Luck of the
Irish (1948) and for
Guess Who's Coming to Dinner (1967)

Puerto Rican-born Jose Ferrer was nominated as Best
Supporting Actor for Joan of Arc (1948)

Shortest and Other Oddities:

The shortest performance time to win a
Best Supporting Actor Oscar was for Anthony Quinn for about nine minutes
as Paul Gaugin in Lust for Life (1956). [The shortest performance
to win an Oscar ever was in the Best Supporting Actress category:
Beatrice Straight won the Best Supporting Actress Oscar for less than
eight minutes of screen time in Network (1976),
with only 8 speaking parts (of approx. 260 words). (Runner up:
Judi Dench for about ten minutes of screen time as Queen Elizabeth in
Shakespeare in Love (1998), with 14 speaking parts (of approx.
446 words).)]

The only diminutive dwarf actor ever nominated for Best Supporting Actor:

Michael Dunn was nominated for Best Supporting Actor for Ship of Fools (1965)

The only Best Supporting Actor winner (and male actor) for a mute performance (in the sound era):

John Mills for his performance as the town idiot Michael in Ryan's Daughter (1970)

Gig Young (with real-name Byron Barr) was the only Oscar winner, Best Supporting Actor for They Shoot Horses, Don't They? (1969), who adopted his screen name from the role he played in The Gay Sisters (1942) as "Gig Young".

Jason Robards has the record for the most
Oscar-nominated roles as historical personages:

Washington Post editor Ben Bradlee in All
The President's Men (1976)

Author Dashiell Hammett in Julia (1977)

Howard Hughes in Melvin and Howard (1980)

Related Oscar Winners and Nominees:
Siblings

The first - and only - brother and sister
to win acting Oscars were:

Lionel Barrymore, who won the Best
Actor award for A Free Soul (1930/31), and Ethel
Barrymore who won the Best Supporting Actress award for None
But the Lonely Heart (1944)(Note:
Famous brother John Barrymore was never nominated, nor has descendant
Drew Barrymore (yet).)

Other brother-sister acting nominees include:

Jane Fonda (nominated seven times with
two Best Actress wins), and Peter Fonda as Best Actor for Ulee's
Gold (1997)

Eric Roberts
as Best Supporting Actor for Runaway Train (1985), and Julia
Roberts (nominated three times with one Best Actress win)

Warren Beatty (nominated four times
for Best Actor with no wins), and Shirley MacLaine (nominated five
times with one Best Actress win)

Jake Gyllenhaal as Best Supporting
Actor for Brokeback Mountain (2005),
and Maggie Gyllenhaal as Best Supporting Actress for Crazy Heart
(2009)

The only brothers nominated for acting
Oscars were:

River Phoenix as Best Supporting Actor for Running
on Empty (1988), and Joaquin Phoenix
as Best Supporting Actor for Gladiator (2000)

Two pairs of sisters have competed against
each other (when nominated simultaneously) for the same Best Actress
award:

Joan Fontaine in Suspicion (1941) defeated
sister Olivia de Havilland in Hold Back the Dawn (1941);
de Havilland later won two Best Actress Oscars for her roles in To
Each His Own (1946) and The Heiress (1949)

The only other sisters to have received acting Oscar
nominations (supporting in this case):

Meg Tilly for Agnes of God (1985) and Jennifer
Tilly for Bullets Over Broadway (1994)

Three Generations:

1948's Oscar-winning director John Huston
directed both his father (Walter Huston) to a Best Supporting Actor
Oscar and his daughter (Anjelica) to a Best Supporting Actress Oscar
in respectively,
The Treasure of the Sierra Madre (1948) and Prizzi's Honor
(1985) 37 years later. [Huston won two Oscars for writing and directing
the 1948 film.] This remarkable feat made the Hustons the first
family with three generations of Oscar winners - Huston became the only
director to have directed both his father and daughter to Oscar victories.
Since Huston also received an acting nomination (supporting) for The
Cardinal (1963), the Hustons are the only grandfather-father-daughter
acting nominees in Oscar history.

In addition, this made the Hustons the only grandfather-granddaughter ever to win Academy Awards:

Anjelica Huston, Best Supporting Actress winner for Prizzi's Honor (1985) (directed by her father John Huston)

A win for Sofia Coppola for Best Original
Screenplay for Lost in Translation (2003) made her part of the
second family of three-generation Oscar winners (her father is
a five-time winner and her grandfather, Carmine Coppola, won for musical
score on The Godfather Part II (1974)). Further connections can be made for the Coppolas - the only father-daughter-nephew grouping to win Oscars:

Sofia Coppola, Best Original Screenplay winner for Lost in Translation (2003)

Nicolas Cage, Best Actor winner for Leaving Las Vegas (1995)

Cast Nominations:

Fifteen films have received nominations
in all four acting categories. With his two films in 2012 and 2013,
director David O. Russell was the first director
to helm two movies (back to back too) that both achieved
this feat:

[Note: Burns was about seven months younger
than 80 year-old Jessica Tandy, who was the oldest winner
of any
acting award, for Driving Miss Daisy (1989).]

Six years (and 310 days) Shirley Temple was the
youngest performer to win an Academy Award when she won an unofficial
honorary 'juvenile' Academy Award statuette in 1934, presented
on February 27, 1935.

94 years (and 341 days) Eli Wallach was the oldest
male performer to receive an honorary statuette in 2010, presented
on November 13, 2010.

85 years (and 215 days) Myrna Loy was the oldest
female performer to receive an honorary statuette in 1990,
presented on March 25, 1991.